Monte Carlo computer simulations were used to investigate the phase behaviour of a Lebwohl-Lasher binary liquid-crystal mixture. A finite-size scaling analysis confirmed the first-order nature of the transition. The calculated nematic-isotopic phase coexistence region and the orientational order parameters for the two species along the phase boundary for a sample system were found to deviate significantly from those predicted by a mean-field theory. Increasing the difference between the isotropic components of the pair-potential of the two species resulted in a broadening of the coexistence region. (C) 1997 Elsevier Science B.V.